Analytical relations for filtering negligible short ship waves

The important basic practical problem of filtering inconsequential short waves that have no significant influence upon the wave drag, the sinkage and the trim experienced by a ship that travels at a constant speed in calm water of large depth is considered. This problem is an essential and nontrivial element of the prediction of ship waves via the use of a Green function that satisfies the linearized boundary condition at the free surface. Simple analytical relations that explicitly determine the wavenumber of insignificant short waves in terms of the Froude number and three main parameters that broadly characterize the ship hull shape are given for ships with bow, midship and stern regions and for ships with wide transoms. These relations are obtained via a parametric numerical analysis, based on the classical Hogner potential flow model, for a wide range of Froude numbers and a large number of hull forms associated with a broad range of hull-shape parameters. The relations provide an effective way of filtering negligible short waves that have no appreciable influence upon the wave drag, the sinkage and the trim of a ship.